How to include vertices to subdivision modifier?
Your biggest problem are these internal faces. I can't really think of a reason you would ever want something like this, so start by deleting them.

The remaining problem, faces have fronts and backs, and the reason you're getting that cusp is because some of your faces are pointing the wrong way.

Select the whole mesh with 'A' and hit 'Shift N' to automatically correct the surface normals.